This paper presents the first formal framework for identifying and filtering SPIT calls (SPam in Internet Telephony) in an outbound scenario with provable optimal performance. In so doing, our work deviates from related earlier work where this problem is only addressed by ad-hoc solutions. Our goal is to rigorously formalize the problem in terms of mathematical decision theory, find the optimal solution to the problem, and derive concrete bounds for its expected loss (number of mistakes the SPIT filter will make in the worst case). This goal is achieved by considering a scenario amenable to theoretical analysis, namely SPIT detection in an outbound scenario with pure sources. Our methodology is to first define the cost of making an error, apply Wald’s sequential probability ratio test, and then determine analytically error probabilities such that the resulting expected loss is minimized. The benefits of our approach are: (1) the method is optimal (in a sense defined in the paper); (2) the method does not rely on manual tuning and tweaking of parameters but is completely self-contained and mathematically justified; (3) the method is computationally simple and scalable. These are desirable features that would make our method a component of choice in larger, autonomic frameworks.